A linearized fitting-based method for determining key pressure parameters in hydraulic fracturing and its applicability evaluatio

To improve the accuracy of identifying key parameters such as instantaneous shut-in pressure (P_s ) and reopening pressure (P_r ) in hydraulic fracturing tests, and to address issues in conventional methods (e.g., tangent method, shifted P_b method, and Muskat method) that are susceptible to noise interference, strong subjectivity, and limited precision when handling nonlinear pressure–time curves, a parameter identification method based on linearized curve fitting is proposed. This method transforms the nonlinear pressure–time curve into multiple locally linear segments through polynomial smoothing and piecewise linear regression, and automatically identifies P_s  and P_r  by detecting abrupt slope changes between adjacent segments. The method was validated through laboratory true triaxial hydraulic fracturing tests on granite specimens and field measurements at the Jizhou pumped storage power station in Tianjin (depth range 75–277 m). Results show that the linearized curve fitting method achieves high accuracy and stability in identifying P_s  and P_r , with significantly reduced average deviation compared to the tangent, shifted P_b , and Muskat methods. Moreover, it demonstrates good robustness under conditions of data disturbance and strong nonlinear responses. This method effectively enhances the objectivity, consistency, and noise resistance of parameter interpretation, is suitable for in-situ stress measurement in hard brittle rock masses, and provides a practical tool for intelligent identification and interpretation of hydraulic fracturing data, with promising engineering application and promotion prospects.